In the very popular movie, "Contact," based on the popular book by Carl Sagan, contact is made with alien's from another world. One thing leads to another and the aliens send a message about Pi. The main character and scientist from the movie, Ellie, does as the message say's and ends up decoding Pi.
Pi has been the obsession of many people, scientists, mathematicians, and nerds in general since Geometry was first discovered.
If you are wondering why by this point it's because Pi is a very strange number. If you didn't already know or forgot, Pi is defined as the circumference of the circle and is rounded off to 3.14159 or just 3.14 for most things. It's really strange in quite a few ways but as far as the decimal is concerned Pi is infinite.
Pi, the circumference of a circle, repeats forever into it's decimal (3.14159 * infinity) as an irrational number. It is, so far as we can tell as a civilization, without logic and therefore unable to be understood or truly computed or measured. Isn't that strange?
So far, Pi has been calculated to more than a trillion decimal places with the use of computers but just about forty decimal is accurate enough to describe distances on subatomic levels, like in the nucleus of an atom, using mathematics.
Pi will work for any circle. The same number is always there out of millions, perhaps billions, of circles people and computers have measured. Pi is also wholly irrational. This is largely the reason why people have become so obsessed with it. Pi has no pattern to it. It's decimal repeat's to infinite so far as anyone or any computer can tell and/as there is no pattern to it. If there was a pattern, or if we discovered a pattern, pi would no longer be irrational and we, as a civilization, could probably solve all physics and math problems to date. That is, the universe would basically be revealed to us. This could also be considered a technological singularity, due to the results it would produce. Unfortunately, as mentioned, no one has figured out Pi in the course of human history and civilization.
Newton, Einstein, and computers are just three great intellects that have been unable to so far solve pi.
Most people who dedicate all or part of their lives to science do so because their core belief's center around the universe being logical, and therefore being able to be understood by humans. Science is essentially a system or method for determining facts. The system of science is and is based on logic (Postulates, theories, hypothesis, deduction, etc...) so it's somewhat embarrassing to have an irrational number such as pi.
The universe is supposed to be rational. If it wasn't how could we ever figure anything out? According to the rules of science, logic can be applied anywhere to figure out or solve a problem. But this hasn't worked with Pi. People have spent their whole lives trying to solve it in vain.
- Contradiction or Duality?
Can you imagine wasting a lifetime trying to solve this?:
A line is equivalent to a minimum of two points.
If you take a string (represented as a line) and fold into a circle then compare the distance around the circle (Circumference) with the original length of the line, then the circle's circumference will be approx. 3.14 (Pi π) times larger than it's diameter.
Unlike squares, triangles, and all angels in general, circles, or any curves for that matter, appear to be irrational in comparison.
If we take any measurable distance within the circle and try to divide it evenly into it's circumference, we will not get a whole number or the number we would expect to get with logic.
Common sense or logic tells us, when viewing the circle, that it can be divided equally into parts. However this is just simply not the case. The parts that we divide a circle into, no matter in how many different ways or combination's, never add up to equal the circumference of the circle.
Hence: The Whole is Greater than the Sum of It's Parts
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